Stability analysis for non-minimally coupled dark energy models in the Palatini formalism

Abstract

In this paper, we use the method of global analysis to study the stability of de-Sitter solutions in an universe dominated by a scalar field dark energy, which couples non-minimally with the Ricci scalar defined in the Palatini formalism. Effective potential and phase-space diagrams are introduced to describe qualitatively the de-Sitter solutions and their stabilities. We find that for the simple power-law function $V(\varphi)=V_{0}\varphi^{n}$ there are no stable de-Sitter solutions. While for some more complicated potentials, i.e. $V(\varphi)=V_{0}\varphi^{n}+\varLambda$ and $V(\varphi)=V_{0} (e ^{-\lambda\varphi}+e^{\lambda\varphi})^{2}$ , stable de-Sitter solutions can exist.